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IUCAA - 2194

July 94

a Automated Classification ofr- w r

C LI1 Ultraviolet Stellar Spectra C

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By

Gulati Ranjan Gupta Pradeep Gothoskar and Shyam Khobragade

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Inter~University-Centre for AstronolllY amp AStrophysics

An Autonomous Institution of the University Grants Commission

Preprint Request (Please quote the preprint number) email preproiucaaemetin

Fax 0212 - 335760 Post IUC~ Post Bag 4 Ganeshkhind Pune 411 007 India

Automated classification of ultraviolet stellar spectra

R K Gulati and Ranjan Gupta IUC~A Post Bag 4 Ganeshkhind Pune 411007 India

gulatiiucaaernetin and ranjan(giucaaernetin

and

Pradeep Gothoskar and Shyam Khobragade J ~M Ly~-

NCRA TIFR Centre PO Box 3 Pune 411007 India pradeepgmrternetin and shyamcggmrternetin

ABSTRACT

The schemes based on the artificial neural networks (ANNs) trained vith multi layer back propagation using single and multi-level tree configurations for classifying ultraviolet spectra in the IUE Low-Dispersion Spectra Reference Atlas have been presented Conventional X2 minimization scheme has also been applied to test the capability of nev methods by comparing the classification obtained from these schemes with that of the catalog classification Preliminary results show that 94 of the test spectra (which were unexposed to the ANNs training sessions) can be classified to an accuracy of the order of one sub-class

Subject headings Stars Stellar Classification Galaxies Stellar Content NIethods Statistical

1 Introduction

Progress in ground based and space instnlIDentation has brought us to a nev era of spectroscopy Large stellar spectral databases through data archives have started becoming available in the wide ravelength range One of the main tasks is to develop fast methods to analyze these spectra and to infer the physical and chemical properties of the stars for understanding the evolutionary processes in the solar neighborhood and other stellar systems One way is to classify the stellar spectra in the light of common visible properties In fact the spectral classification is a useful tool not only to arrange the spectra of the stars into meaningful and self consistent groups but also for proYiding information about

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the astrophysical parameters namely effective temperature luminosity mass and radius etc The distribution of the stars in the various groups can be used for the statistical study of stellar populations in the solar neighborhood and for other stellar systems which are increasingly becoming accessible through spectroscopic studies A comprehensive review on the subject of stellar classification has been made by (Jaschek and Jaschek (1990))

Conventionally stellar classification used to be done by the visual inspection of the individual stellar spectra by the human experts and this approach led to many non-unique data bases with inherent biases of the human classifiers In contrast to this manual scheme of classification the automated classification schemes have numerous advantages viz high speed on line classification homogeneity (elimination of personal error) accuracy detection of variability and possibility of classification of higher dimension

There are two approaches to perform the automated classification criteria evaluation and pattern recognition In the first case a set of specified criteria such as the width or strength of specified lines are automatically measured and then calibrated in tenus of the desired quantities (eg spectral types and luminosity class)

On the other hand in pattern recognition an observed spectrum is compared with a library of reference spectra following a cross-correlation scheme or multi variant statistical methods These techniques have their limitations for example the cross-correlation technique (Adorf (1986)) is limited due to the fact that the weights are given to the strong lines which may not be the diagnostic of the spectral classes Nloreover these techniques are based on linear operations whereas the inter-relation among the parameters effecting the stellar spectra can actually be non-linear and thus one requires a technique which can handle this type of relationship The Artificial Neural Networks (ANN) scheme vhich forms the main theme of this meeting is of non-linear nature and this makes it well suited for complex morphological classification jobs like spectral classification

The schemes discussed above have to be automated for projects involving classification of large databases as these require higher degree of efficiency which has to be achieved without any manual intervention The Anglo-Australian Telescope (AAT) multi-object spectrograph will provide lots of new digital data and perhaps a quick-look approach could be provided automatically followed by a more careful study of the most interesting stars Automated stellar spectral classification using ANN technique has been recently achieved in the optical and the near infra-red (Nffi) wavelength region in recent times (von Hippel et al (1994) Gulati et al (1994) and Veaver (1994)) However in the ultra-violet (UV) region only conventional statistical methods of classification have been tested on existing catalogs ( Jaschek and Jaschek(1984) and Heck et al (1986)) The UV region of the spectrum is very inlportant in the understanding of the early type stars as they exhibit

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most of there fllDces in the UT Further the comparison of the UV spectral classification vith that of its optical counterpart can resolve the anomalies of classification and supplement information on interstellar etinction (Gulati et al (1987)) 1vloreover detectors have been vastly improved which in turn allow access to wavelength regions which were not possible to observe earlier In the ultra violet (UT) region the spectral data has been gathered with satellite based platforms of which the IUE satellite has been the most successful mission For details on the IUE instruments readers are referred to the article by (Boggess et ale (1978a) (1978b)) This satellite has been providing us with homogeneous library of UV stellar spectra in low and high dispersions It is capable of observing distant stellar objects which would otherwise require much larger ground based telescope times

Our earlier experience of successfully applying the ANN technique to visible spectra motivated us to test it on the UV database and in this paper we present the preliminary results of the UV spectral classification

The paper is organized as follows In section 2 we discuss the input data and its pre-processing while in section 3 the classification schemes based on X2- minimization and ANNs are presented Section 4 gives the results and discussion and finally section ) contains the conclusions

2 The input data and pre-processing

The database used for this work is the IDE Low resolution spectra reference atlas Normal Stars ESA SP-1052 by (Heck et ale (1984)) which has 229 low dispersion spectra (spanning 0 to K spectral types) collected by the International Ultraviolet Explorer (IDE) satellite Since this catalog contains biased samples of different spectral classes with insufficient late type spectra we have restricted ourselves from 0 to early F type spectra Further the luminosity classes have been restricted to super-giants giants and dwarfs due to inadequate samples for finer subdivisions of luminosity classes This criterion has led us to select a total of 211 spectra from this catalog of which a subset of 128 spectra spanning 75 spectro-luminosity classes (0 to F) form the training set and the remaining 83 form the test set The selection of the training set was made by avoiding as far as possible the cases where interstellar extinction was high so that the interstellar reddening does not affect the continuum For the proper training of the neural network each spectro-luminosity class must have at least two patterns (ie 150 patterns for training) and for this purpose some spectro-luminosity types which had only one example had to be duplicated for the training session The catalog classification for the spectra were taken from (Heck et ale (1984)) where the UV spectral classiiication is given in terms of OBA and F (main classes)

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sub-classes (00 to 93) and luminosity (super-giants giant darfs etc) The spectra cover the range of 1213-3201 A with one sample per 2 A (spectral resolution of IV 6 A ) ie 995 data points All the spectra were normalized such that the maamum flux in each corresponds to unity for the sake of uniformity and this ensures that the line and continuum information are included in the sample

Conventionally spectro-luminosity class is named in an alpha-numeric fashion and by using an integer code one can simplify the process of data-coding into a computer Ve have coded the spectro-luminosity classes into a four-digit number for the purpose of quantitative analysis of the classification as follows

CODE NU~mER = 1000 X Al + 100 X A2 + A3 (1)

where Al is the main spectral type of the star (ie 0 to F types coded as 1 to 4) A2 is the sub-spectral type of the star (coded from 00 to 95) and A3 the luminosity class of the star (ie 2 5 or 8 for s g or d) As an example in our scheme of numbering stars having spectro-luminosity classes dB25 g095 and sF7 (ultraviolet classes) would be coded as 2258 1955 and 4702 respectively

Each spectro-luminosity class is characterized by a set of absorption features appearing at a few knoTD wavelengths which are also the diagnostic of the spectral type (Heck et al (1986) Table I) and therefore useful for the UV spectral classification Ve have used the line depths at these selected wavelengths (a total of 35 different positions within the spectral range of interest) This improves the efficiency of the network as compared to allowing the full spectra of 995 datapoints for training the ANN Figure 1 sho~s the typical stellar UV spectra for OBA and F type stars along with the wavelength positions here the line depths (flux values) are monitored for ANN training and test sessions In this figure we have purposely offset each spectrum in order to display them without any overlapping and thus the intensity scale is set to arbitrary units It is evident from the figure that the early type stars have higher flux values in the shorter wavelength region but the number of spectral features increases and tends to concentrate in the longer wavelength region for the late type stars

3 Classification Schemes

31 Metric Distance Minimization Scheme

The metric distance minimization scheme (also known as mjnimum vector distance) has been well reviewed by (Kurtz (1984)) and 7Ire have used his scheme (hereafter referred

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to as x2-minimization scheme) on the IUE data only for comparing the performance of the ANN techniques This technique is based on the assumption that the spectrum consists of points in an n-dimensional vector space (where n is approximately the number of resolution elements in the spectrum) and the classification is based on finding the shortest distance from the unknown stars spectrum to a set of spectra of the standard stars The view of the observation space as a vector space lies at the heart of the various parametric methods of statistical comparison such as techniques based on reduced X2 which is defined as (for no statistical weighting Bevington (1969))

x2= Ef=l(S - Tt)2 (2)P

where p is equal to the degrees of freedom SiCA) is the spectrum for one of the set of standard star spectra and Ti(Ai) for the unknown stars spectrum Ai are the wavelengths with i = 1 n for n wavelength monitoring points as is described later in the paper The unknown stars spectrum (test spectrum) is compared with the set of reference spectra to compute a set of X2 values The spectral type of the reference spectrum corresponding to the minirrium X2 is assigned to the test spectrum This procedure is then repeated for the remaining set of the test spectra

32 Artificial Neural Networks Scheme

Artificial neural networks (hereafter ANNs) are computational models derived from the simulation of the human brain (IvlcCulloch and Pitts (1943) and Hopfield and Tank (1986)) These netrorks consist of a series of processing elements known as neurons or nodes arranged in layers These nodes are analogous to biological neurons with inputs (dendrites) summing nodes (soma or cell bodies) outputs (axons) and weighted connections between layers (synapses)

These networks have ability to learn from examples and store the information in weights in a generalized form This facilitates the appropriate classification ~f the input patterns which are not included in the training set provided the training set covered the representative patterns for all the claSses The features of ANN learning and generalization thus enable these networks for solving imaging and signal processing tasks which cannot be readily attacked using rule-based or other conventional techniques

Various ANN architectures and learning algorithms have been developed and are being used in academic research as well as in industrial applications A plenty of books and research papers onthis topic are available A few network architectures and learning rules have been reviewed by (Adorf (1989) Vidrow and Lehr (1990) and Clark (1991))

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Recently ANN algorithms are being used for arious astronomy applications including the classification of objects in the mAS Point Source Catalogue (Adorf and IYleurs (1988)) adaptive optics (Angel et al (1990)) star-galaxy separation (Odewahn et al (1992)) stellar spectral classification (von Hippel et al (1994) Gulati et al (1994)) morphological classification of galaxies (Storrie-Lombardi et al (1992)) and classification of interplanetary spectra (Gothoskar and Khobragade (1993)) IYlost of these astronomy applications using ANNs have been reviewed by (lfi11er (1993))

In astronomy applications so far researchers have used mainly two types of learning algorithms - a supervised backpropagation network (Rumelhart et al (1986)) and an unsupervised self-organizing map (Kohonen (1990)) Hybrid models using both strategies with and without supervision have also been developed such as the counter-propagation network (Hecht-Nielson (1987)) which are not yet employed in astronomy There are other models like hierarchical networks and tree networks (Sankar and IYlammone (1991)) 1

which are still away from the astronomy field Supervised learning requires researchers desired response during training which means these networks learn in supervision of the researcher Unsupervised learning requires no exemplar output or supervision

For this application we have investigated a conventional backpropagation network (hereafter IYIBPN) as a pattern classifier to discriminate the IDE stellar spectra into arious classes Ve have also attempted a tree-like network we call it as a multilevel tree network (hereafter IYITN) which employs the IYffiPN at the root and each non-terminal nodes of the tree

3 Bl The multilayer bac1cpropagation clGSsifier

The multilayer backpropagation network (Rumelhart et al (1986)) has several nodes arranged in a series of layers - an input layer one or more hidden layers and an output layer Input layer equals the size of the input pattern and the size of output layer is equal to the number of classes to be distinguished The size of the intermediate layers depends on the complexity of the problem to be solved The intermediate layers are also known as hidden lay~rs The network complexity is a function of the number of inputs hidden nodes layers outputs and connections (see Figure 2) It should be noted that the input layer is transparent in the sense that it receives the input pattern and distributes it to the next layer as it is without doing any computations The weighted connections between the layers are unidirectional and the information flows from the input layer through the output layer Hence it is also called a feedforward network A layer is fully connected if each node in the layer is connected to all the nodes in an adjacent layer However the complexity of

the netYork can be reduced by using partially connected layers

Learning the network means to find a set of weights which eventually store the learned patterns During learning the weights are first initialized to small random values The input pattern from the training set is then presented to the network The weighted input is summed over linearly at each node of the hidden layer and is passed through a non-linear sigmoid transfer function to get an actual output at each node using the existing set of weights The procedure is repeated for all the nodes in the hidden and output layers The resultant computed output is then compared with the desired output to get an error term which is propagated backward through the network to compute the changes of the interconnection Yeights between each pair of layers The weights are updated in such a way as to mjnimize the output error during the next time-step of the learning process The procedure is repeated for all the patterns in the training set and the weights are updated until the network output error mjnimizes to the specified threshold value The rate of updating of weights is controlled by a learning coefficient (gain factor) and a momentum factor a which damps the oscillations in the error minjmization process and furthermore both these parameters are dependent on the input patterns Veights can be updated after presenting each input pattern or after each presentation of the complete training set A plot of the error term against the number of presentations gives a learning curve~ which ideally converges to zerO as the number of presentations increases A training set consists of a variety of examples from each class to generalize the class information which is eventually stored in the weights The final set of weights are used to classify a large database which was not used during training

922 The multilevel tree network

Ve have attempted a new technique resembling a tree structure A three-level tree network is shown in Figure 3 This network terminology is analogous to that ofmiddota tree The very first node is called a root node which is at level one Nodes at level two which are children of root node again form subtrees Terminal nodes which are at last level are also called leaf nodes Children of the same parent node are known as siblings

The 1ITN uses the same 1ffiPN (described above) at root and non-terminal nodes Terminal nodes just label the final output class they do not employ the 1IBPN classifier

The learning algorithm for this network is derived as follows A complete training set is presented to the root node The classifier at the root node discrinlinates the whole training set into the main classes of different spectral types The outputs of the root node

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classifier represented as non-terminal nodes (see Figure 3) further use the lVIBPN over the reduced training set containing only the respective main-class spectra The siblings at level two can be computed conctUrently on different machines (if one has access to a netYork of work stations) The output of each individual sibling classifier which are represented by leaf nodes are used to label the class of the input pattern The yeights of root and siblings classifiers can be stored in separate files to use them for the application to unseen database

DtUing the application of this network the test pattern is first presented to the root node classifier which classifies it as one of the main classes Then the same pattern is applied to the respective class-sibling classifier to classify it to a sub-class type

The root and the sibling classifiers are configured depending on the input size and the number of classes- to be discriminated at each level This network as a whole is a supervised network which means the network is trained according to the desired response of the researcher

In this paper we have investigated these two methods of ANN for the classification of ruE stellar spectra The first method involves a single IvIBPN classifier to classify the test spectra into 75 spectro-luminosity classes The second method which in principle incorporates a divide-and-conquer technique is devised as a tree network The root node distinguishes the database into four main spectral types and then its children nodes further classified it into a total of 75 spectro-luminosity classes

In the first case the whole training set was presented to the network several times dtUing training until the network was able to discriminate all 75 classes In the case of the tree network the whole training set was presented to the root node to classify only four main spectral classes and then the subset of training set was presented to each sibling network to further classify it into sub-classes This tree network can be extended further to find many sub-class types if the database of any application provides the p~tterns upto those many sub-class types One advantage of IvITN over ANN is that it requires lesser time than ANN since after the initial root node classification it has to only classify the sibling nodes

4 Results and Discussion

Ve applied ANN comprising the 35 input nodes (n=35 monitoring frequency parameters) one hidden layer of (2n+l) nodes and outputs of 75 nodes representing the 75

spectro-luminosity classes to train the network The (2n+l) criterion is dictated by certain empirical facts and theoretical considerations which render an optimization on accuracy

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human ePerts

5 Conclusion

Ve have demonstrated that Neural Networks schemes based on multi layer back propagation method using single and multi-level tree configllrationsare able to classify 94 of the test sample of lTV spectra to one-sub class accuracy_ Vith these schemes 72 of the spectra were classified correctly in terms of luminosity which is otherwise a sore point of automated schemes Further improvement is required in the training part of the ANNs which should ultimately lead to greater classification accuracies ANNs will beconle

extremely handy for large database classifications which are otherwise outside the scope of human classification

Ve thank the ruCAA Astronomical Data Center for providing the spectral catalogs used in the current work Thanks are also due to Profs C Jaschek and lV1 Jaschek for their useful comments Ve are grateful to Prof K D Abhyankar for critically going through the manuscript This research has made use of the SIlVIBAD database operated at CDS Strasbourg France

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Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

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REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

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Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

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Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

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Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

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most of there fllDces in the UT Further the comparison of the UV spectral classification vith that of its optical counterpart can resolve the anomalies of classification and supplement information on interstellar etinction (Gulati et al (1987)) 1vloreover detectors have been vastly improved which in turn allow access to wavelength regions which were not possible to observe earlier In the ultra violet (UT) region the spectral data has been gathered with satellite based platforms of which the IUE satellite has been the most successful mission For details on the IUE instruments readers are referred to the article by (Boggess et ale (1978a) (1978b)) This satellite has been providing us with homogeneous library of UV stellar spectra in low and high dispersions It is capable of observing distant stellar objects which would otherwise require much larger ground based telescope times

Our earlier experience of successfully applying the ANN technique to visible spectra motivated us to test it on the UV database and in this paper we present the preliminary results of the UV spectral classification

The paper is organized as follows In section 2 we discuss the input data and its pre-processing while in section 3 the classification schemes based on X2- minimization and ANNs are presented Section 4 gives the results and discussion and finally section ) contains the conclusions

2 The input data and pre-processing

The database used for this work is the IDE Low resolution spectra reference atlas Normal Stars ESA SP-1052 by (Heck et ale (1984)) which has 229 low dispersion spectra (spanning 0 to K spectral types) collected by the International Ultraviolet Explorer (IDE) satellite Since this catalog contains biased samples of different spectral classes with insufficient late type spectra we have restricted ourselves from 0 to early F type spectra Further the luminosity classes have been restricted to super-giants giants and dwarfs due to inadequate samples for finer subdivisions of luminosity classes This criterion has led us to select a total of 211 spectra from this catalog of which a subset of 128 spectra spanning 75 spectro-luminosity classes (0 to F) form the training set and the remaining 83 form the test set The selection of the training set was made by avoiding as far as possible the cases where interstellar extinction was high so that the interstellar reddening does not affect the continuum For the proper training of the neural network each spectro-luminosity class must have at least two patterns (ie 150 patterns for training) and for this purpose some spectro-luminosity types which had only one example had to be duplicated for the training session The catalog classification for the spectra were taken from (Heck et ale (1984)) where the UV spectral classiiication is given in terms of OBA and F (main classes)

-4shy

sub-classes (00 to 93) and luminosity (super-giants giant darfs etc) The spectra cover the range of 1213-3201 A with one sample per 2 A (spectral resolution of IV 6 A ) ie 995 data points All the spectra were normalized such that the maamum flux in each corresponds to unity for the sake of uniformity and this ensures that the line and continuum information are included in the sample

Conventionally spectro-luminosity class is named in an alpha-numeric fashion and by using an integer code one can simplify the process of data-coding into a computer Ve have coded the spectro-luminosity classes into a four-digit number for the purpose of quantitative analysis of the classification as follows

CODE NU~mER = 1000 X Al + 100 X A2 + A3 (1)

where Al is the main spectral type of the star (ie 0 to F types coded as 1 to 4) A2 is the sub-spectral type of the star (coded from 00 to 95) and A3 the luminosity class of the star (ie 2 5 or 8 for s g or d) As an example in our scheme of numbering stars having spectro-luminosity classes dB25 g095 and sF7 (ultraviolet classes) would be coded as 2258 1955 and 4702 respectively

Each spectro-luminosity class is characterized by a set of absorption features appearing at a few knoTD wavelengths which are also the diagnostic of the spectral type (Heck et al (1986) Table I) and therefore useful for the UV spectral classification Ve have used the line depths at these selected wavelengths (a total of 35 different positions within the spectral range of interest) This improves the efficiency of the network as compared to allowing the full spectra of 995 datapoints for training the ANN Figure 1 sho~s the typical stellar UV spectra for OBA and F type stars along with the wavelength positions here the line depths (flux values) are monitored for ANN training and test sessions In this figure we have purposely offset each spectrum in order to display them without any overlapping and thus the intensity scale is set to arbitrary units It is evident from the figure that the early type stars have higher flux values in the shorter wavelength region but the number of spectral features increases and tends to concentrate in the longer wavelength region for the late type stars

3 Classification Schemes

31 Metric Distance Minimization Scheme

The metric distance minimization scheme (also known as mjnimum vector distance) has been well reviewed by (Kurtz (1984)) and 7Ire have used his scheme (hereafter referred

-5shy

to as x2-minimization scheme) on the IUE data only for comparing the performance of the ANN techniques This technique is based on the assumption that the spectrum consists of points in an n-dimensional vector space (where n is approximately the number of resolution elements in the spectrum) and the classification is based on finding the shortest distance from the unknown stars spectrum to a set of spectra of the standard stars The view of the observation space as a vector space lies at the heart of the various parametric methods of statistical comparison such as techniques based on reduced X2 which is defined as (for no statistical weighting Bevington (1969))

x2= Ef=l(S - Tt)2 (2)P

where p is equal to the degrees of freedom SiCA) is the spectrum for one of the set of standard star spectra and Ti(Ai) for the unknown stars spectrum Ai are the wavelengths with i = 1 n for n wavelength monitoring points as is described later in the paper The unknown stars spectrum (test spectrum) is compared with the set of reference spectra to compute a set of X2 values The spectral type of the reference spectrum corresponding to the minirrium X2 is assigned to the test spectrum This procedure is then repeated for the remaining set of the test spectra

32 Artificial Neural Networks Scheme

Artificial neural networks (hereafter ANNs) are computational models derived from the simulation of the human brain (IvlcCulloch and Pitts (1943) and Hopfield and Tank (1986)) These netrorks consist of a series of processing elements known as neurons or nodes arranged in layers These nodes are analogous to biological neurons with inputs (dendrites) summing nodes (soma or cell bodies) outputs (axons) and weighted connections between layers (synapses)

These networks have ability to learn from examples and store the information in weights in a generalized form This facilitates the appropriate classification ~f the input patterns which are not included in the training set provided the training set covered the representative patterns for all the claSses The features of ANN learning and generalization thus enable these networks for solving imaging and signal processing tasks which cannot be readily attacked using rule-based or other conventional techniques

Various ANN architectures and learning algorithms have been developed and are being used in academic research as well as in industrial applications A plenty of books and research papers onthis topic are available A few network architectures and learning rules have been reviewed by (Adorf (1989) Vidrow and Lehr (1990) and Clark (1991))

5

-6shy

Recently ANN algorithms are being used for arious astronomy applications including the classification of objects in the mAS Point Source Catalogue (Adorf and IYleurs (1988)) adaptive optics (Angel et al (1990)) star-galaxy separation (Odewahn et al (1992)) stellar spectral classification (von Hippel et al (1994) Gulati et al (1994)) morphological classification of galaxies (Storrie-Lombardi et al (1992)) and classification of interplanetary spectra (Gothoskar and Khobragade (1993)) IYlost of these astronomy applications using ANNs have been reviewed by (lfi11er (1993))

In astronomy applications so far researchers have used mainly two types of learning algorithms - a supervised backpropagation network (Rumelhart et al (1986)) and an unsupervised self-organizing map (Kohonen (1990)) Hybrid models using both strategies with and without supervision have also been developed such as the counter-propagation network (Hecht-Nielson (1987)) which are not yet employed in astronomy There are other models like hierarchical networks and tree networks (Sankar and IYlammone (1991)) 1

which are still away from the astronomy field Supervised learning requires researchers desired response during training which means these networks learn in supervision of the researcher Unsupervised learning requires no exemplar output or supervision

For this application we have investigated a conventional backpropagation network (hereafter IYIBPN) as a pattern classifier to discriminate the IDE stellar spectra into arious classes Ve have also attempted a tree-like network we call it as a multilevel tree network (hereafter IYITN) which employs the IYffiPN at the root and each non-terminal nodes of the tree

3 Bl The multilayer bac1cpropagation clGSsifier

The multilayer backpropagation network (Rumelhart et al (1986)) has several nodes arranged in a series of layers - an input layer one or more hidden layers and an output layer Input layer equals the size of the input pattern and the size of output layer is equal to the number of classes to be distinguished The size of the intermediate layers depends on the complexity of the problem to be solved The intermediate layers are also known as hidden lay~rs The network complexity is a function of the number of inputs hidden nodes layers outputs and connections (see Figure 2) It should be noted that the input layer is transparent in the sense that it receives the input pattern and distributes it to the next layer as it is without doing any computations The weighted connections between the layers are unidirectional and the information flows from the input layer through the output layer Hence it is also called a feedforward network A layer is fully connected if each node in the layer is connected to all the nodes in an adjacent layer However the complexity of

the netYork can be reduced by using partially connected layers

Learning the network means to find a set of weights which eventually store the learned patterns During learning the weights are first initialized to small random values The input pattern from the training set is then presented to the network The weighted input is summed over linearly at each node of the hidden layer and is passed through a non-linear sigmoid transfer function to get an actual output at each node using the existing set of weights The procedure is repeated for all the nodes in the hidden and output layers The resultant computed output is then compared with the desired output to get an error term which is propagated backward through the network to compute the changes of the interconnection Yeights between each pair of layers The weights are updated in such a way as to mjnimize the output error during the next time-step of the learning process The procedure is repeated for all the patterns in the training set and the weights are updated until the network output error mjnimizes to the specified threshold value The rate of updating of weights is controlled by a learning coefficient (gain factor) and a momentum factor a which damps the oscillations in the error minjmization process and furthermore both these parameters are dependent on the input patterns Veights can be updated after presenting each input pattern or after each presentation of the complete training set A plot of the error term against the number of presentations gives a learning curve~ which ideally converges to zerO as the number of presentations increases A training set consists of a variety of examples from each class to generalize the class information which is eventually stored in the weights The final set of weights are used to classify a large database which was not used during training

922 The multilevel tree network

Ve have attempted a new technique resembling a tree structure A three-level tree network is shown in Figure 3 This network terminology is analogous to that ofmiddota tree The very first node is called a root node which is at level one Nodes at level two which are children of root node again form subtrees Terminal nodes which are at last level are also called leaf nodes Children of the same parent node are known as siblings

The 1ITN uses the same 1ffiPN (described above) at root and non-terminal nodes Terminal nodes just label the final output class they do not employ the 1IBPN classifier

The learning algorithm for this network is derived as follows A complete training set is presented to the root node The classifier at the root node discrinlinates the whole training set into the main classes of different spectral types The outputs of the root node

7

-8shy

classifier represented as non-terminal nodes (see Figure 3) further use the lVIBPN over the reduced training set containing only the respective main-class spectra The siblings at level two can be computed conctUrently on different machines (if one has access to a netYork of work stations) The output of each individual sibling classifier which are represented by leaf nodes are used to label the class of the input pattern The yeights of root and siblings classifiers can be stored in separate files to use them for the application to unseen database

DtUing the application of this network the test pattern is first presented to the root node classifier which classifies it as one of the main classes Then the same pattern is applied to the respective class-sibling classifier to classify it to a sub-class type

The root and the sibling classifiers are configured depending on the input size and the number of classes- to be discriminated at each level This network as a whole is a supervised network which means the network is trained according to the desired response of the researcher

In this paper we have investigated these two methods of ANN for the classification of ruE stellar spectra The first method involves a single IvIBPN classifier to classify the test spectra into 75 spectro-luminosity classes The second method which in principle incorporates a divide-and-conquer technique is devised as a tree network The root node distinguishes the database into four main spectral types and then its children nodes further classified it into a total of 75 spectro-luminosity classes

In the first case the whole training set was presented to the network several times dtUing training until the network was able to discriminate all 75 classes In the case of the tree network the whole training set was presented to the root node to classify only four main spectral classes and then the subset of training set was presented to each sibling network to further classify it into sub-classes This tree network can be extended further to find many sub-class types if the database of any application provides the p~tterns upto those many sub-class types One advantage of IvITN over ANN is that it requires lesser time than ANN since after the initial root node classification it has to only classify the sibling nodes

4 Results and Discussion

Ve applied ANN comprising the 35 input nodes (n=35 monitoring frequency parameters) one hidden layer of (2n+l) nodes and outputs of 75 nodes representing the 75

spectro-luminosity classes to train the network The (2n+l) criterion is dictated by certain empirical facts and theoretical considerations which render an optimization on accuracy

- 11 shy

human ePerts

5 Conclusion

Ve have demonstrated that Neural Networks schemes based on multi layer back propagation method using single and multi-level tree configllrationsare able to classify 94 of the test sample of lTV spectra to one-sub class accuracy_ Vith these schemes 72 of the spectra were classified correctly in terms of luminosity which is otherwise a sore point of automated schemes Further improvement is required in the training part of the ANNs which should ultimately lead to greater classification accuracies ANNs will beconle

extremely handy for large database classifications which are otherwise outside the scope of human classification

Ve thank the ruCAA Astronomical Data Center for providing the spectral catalogs used in the current work Thanks are also due to Profs C Jaschek and lV1 Jaschek for their useful comments Ve are grateful to Prof K D Abhyankar for critically going through the manuscript This research has made use of the SIlVIBAD database operated at CDS Strasbourg France

- 12shy

Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

5000

4000

3000 zz lt

2000

1000

0 a 1000 2000 3000

Catalog 4000 5000

5000

4000

3000 z ~

2000

1000

a ~--~~~~~--~--~--~--~--~ a 1000 2000 3000 4000 5000

Catalog

50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

4000 40

rIJ

laquoS 3000 j 30

~ 0

2000 eQJ

20 = z

1000

1000 2000 3000 4000 5000

10

a

f

Catalog

5000

4000

3000

~

2000

1000

0 B A F a

-1000 -500 a 500 1000 Deviation (r)

50

40

f laquoS j 30 0 eQJ

20 s z

10

a

h

a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

60 60

In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

-4shy

sub-classes (00 to 93) and luminosity (super-giants giant darfs etc) The spectra cover the range of 1213-3201 A with one sample per 2 A (spectral resolution of IV 6 A ) ie 995 data points All the spectra were normalized such that the maamum flux in each corresponds to unity for the sake of uniformity and this ensures that the line and continuum information are included in the sample

Conventionally spectro-luminosity class is named in an alpha-numeric fashion and by using an integer code one can simplify the process of data-coding into a computer Ve have coded the spectro-luminosity classes into a four-digit number for the purpose of quantitative analysis of the classification as follows

CODE NU~mER = 1000 X Al + 100 X A2 + A3 (1)

where Al is the main spectral type of the star (ie 0 to F types coded as 1 to 4) A2 is the sub-spectral type of the star (coded from 00 to 95) and A3 the luminosity class of the star (ie 2 5 or 8 for s g or d) As an example in our scheme of numbering stars having spectro-luminosity classes dB25 g095 and sF7 (ultraviolet classes) would be coded as 2258 1955 and 4702 respectively

Each spectro-luminosity class is characterized by a set of absorption features appearing at a few knoTD wavelengths which are also the diagnostic of the spectral type (Heck et al (1986) Table I) and therefore useful for the UV spectral classification Ve have used the line depths at these selected wavelengths (a total of 35 different positions within the spectral range of interest) This improves the efficiency of the network as compared to allowing the full spectra of 995 datapoints for training the ANN Figure 1 sho~s the typical stellar UV spectra for OBA and F type stars along with the wavelength positions here the line depths (flux values) are monitored for ANN training and test sessions In this figure we have purposely offset each spectrum in order to display them without any overlapping and thus the intensity scale is set to arbitrary units It is evident from the figure that the early type stars have higher flux values in the shorter wavelength region but the number of spectral features increases and tends to concentrate in the longer wavelength region for the late type stars

3 Classification Schemes

31 Metric Distance Minimization Scheme

The metric distance minimization scheme (also known as mjnimum vector distance) has been well reviewed by (Kurtz (1984)) and 7Ire have used his scheme (hereafter referred

-5shy

to as x2-minimization scheme) on the IUE data only for comparing the performance of the ANN techniques This technique is based on the assumption that the spectrum consists of points in an n-dimensional vector space (where n is approximately the number of resolution elements in the spectrum) and the classification is based on finding the shortest distance from the unknown stars spectrum to a set of spectra of the standard stars The view of the observation space as a vector space lies at the heart of the various parametric methods of statistical comparison such as techniques based on reduced X2 which is defined as (for no statistical weighting Bevington (1969))

x2= Ef=l(S - Tt)2 (2)P

where p is equal to the degrees of freedom SiCA) is the spectrum for one of the set of standard star spectra and Ti(Ai) for the unknown stars spectrum Ai are the wavelengths with i = 1 n for n wavelength monitoring points as is described later in the paper The unknown stars spectrum (test spectrum) is compared with the set of reference spectra to compute a set of X2 values The spectral type of the reference spectrum corresponding to the minirrium X2 is assigned to the test spectrum This procedure is then repeated for the remaining set of the test spectra

32 Artificial Neural Networks Scheme

Artificial neural networks (hereafter ANNs) are computational models derived from the simulation of the human brain (IvlcCulloch and Pitts (1943) and Hopfield and Tank (1986)) These netrorks consist of a series of processing elements known as neurons or nodes arranged in layers These nodes are analogous to biological neurons with inputs (dendrites) summing nodes (soma or cell bodies) outputs (axons) and weighted connections between layers (synapses)

These networks have ability to learn from examples and store the information in weights in a generalized form This facilitates the appropriate classification ~f the input patterns which are not included in the training set provided the training set covered the representative patterns for all the claSses The features of ANN learning and generalization thus enable these networks for solving imaging and signal processing tasks which cannot be readily attacked using rule-based or other conventional techniques

Various ANN architectures and learning algorithms have been developed and are being used in academic research as well as in industrial applications A plenty of books and research papers onthis topic are available A few network architectures and learning rules have been reviewed by (Adorf (1989) Vidrow and Lehr (1990) and Clark (1991))

5

-6shy

Recently ANN algorithms are being used for arious astronomy applications including the classification of objects in the mAS Point Source Catalogue (Adorf and IYleurs (1988)) adaptive optics (Angel et al (1990)) star-galaxy separation (Odewahn et al (1992)) stellar spectral classification (von Hippel et al (1994) Gulati et al (1994)) morphological classification of galaxies (Storrie-Lombardi et al (1992)) and classification of interplanetary spectra (Gothoskar and Khobragade (1993)) IYlost of these astronomy applications using ANNs have been reviewed by (lfi11er (1993))

In astronomy applications so far researchers have used mainly two types of learning algorithms - a supervised backpropagation network (Rumelhart et al (1986)) and an unsupervised self-organizing map (Kohonen (1990)) Hybrid models using both strategies with and without supervision have also been developed such as the counter-propagation network (Hecht-Nielson (1987)) which are not yet employed in astronomy There are other models like hierarchical networks and tree networks (Sankar and IYlammone (1991)) 1

which are still away from the astronomy field Supervised learning requires researchers desired response during training which means these networks learn in supervision of the researcher Unsupervised learning requires no exemplar output or supervision

For this application we have investigated a conventional backpropagation network (hereafter IYIBPN) as a pattern classifier to discriminate the IDE stellar spectra into arious classes Ve have also attempted a tree-like network we call it as a multilevel tree network (hereafter IYITN) which employs the IYffiPN at the root and each non-terminal nodes of the tree

3 Bl The multilayer bac1cpropagation clGSsifier

The multilayer backpropagation network (Rumelhart et al (1986)) has several nodes arranged in a series of layers - an input layer one or more hidden layers and an output layer Input layer equals the size of the input pattern and the size of output layer is equal to the number of classes to be distinguished The size of the intermediate layers depends on the complexity of the problem to be solved The intermediate layers are also known as hidden lay~rs The network complexity is a function of the number of inputs hidden nodes layers outputs and connections (see Figure 2) It should be noted that the input layer is transparent in the sense that it receives the input pattern and distributes it to the next layer as it is without doing any computations The weighted connections between the layers are unidirectional and the information flows from the input layer through the output layer Hence it is also called a feedforward network A layer is fully connected if each node in the layer is connected to all the nodes in an adjacent layer However the complexity of

the netYork can be reduced by using partially connected layers

Learning the network means to find a set of weights which eventually store the learned patterns During learning the weights are first initialized to small random values The input pattern from the training set is then presented to the network The weighted input is summed over linearly at each node of the hidden layer and is passed through a non-linear sigmoid transfer function to get an actual output at each node using the existing set of weights The procedure is repeated for all the nodes in the hidden and output layers The resultant computed output is then compared with the desired output to get an error term which is propagated backward through the network to compute the changes of the interconnection Yeights between each pair of layers The weights are updated in such a way as to mjnimize the output error during the next time-step of the learning process The procedure is repeated for all the patterns in the training set and the weights are updated until the network output error mjnimizes to the specified threshold value The rate of updating of weights is controlled by a learning coefficient (gain factor) and a momentum factor a which damps the oscillations in the error minjmization process and furthermore both these parameters are dependent on the input patterns Veights can be updated after presenting each input pattern or after each presentation of the complete training set A plot of the error term against the number of presentations gives a learning curve~ which ideally converges to zerO as the number of presentations increases A training set consists of a variety of examples from each class to generalize the class information which is eventually stored in the weights The final set of weights are used to classify a large database which was not used during training

922 The multilevel tree network

Ve have attempted a new technique resembling a tree structure A three-level tree network is shown in Figure 3 This network terminology is analogous to that ofmiddota tree The very first node is called a root node which is at level one Nodes at level two which are children of root node again form subtrees Terminal nodes which are at last level are also called leaf nodes Children of the same parent node are known as siblings

The 1ITN uses the same 1ffiPN (described above) at root and non-terminal nodes Terminal nodes just label the final output class they do not employ the 1IBPN classifier

The learning algorithm for this network is derived as follows A complete training set is presented to the root node The classifier at the root node discrinlinates the whole training set into the main classes of different spectral types The outputs of the root node

7

-8shy

classifier represented as non-terminal nodes (see Figure 3) further use the lVIBPN over the reduced training set containing only the respective main-class spectra The siblings at level two can be computed conctUrently on different machines (if one has access to a netYork of work stations) The output of each individual sibling classifier which are represented by leaf nodes are used to label the class of the input pattern The yeights of root and siblings classifiers can be stored in separate files to use them for the application to unseen database

DtUing the application of this network the test pattern is first presented to the root node classifier which classifies it as one of the main classes Then the same pattern is applied to the respective class-sibling classifier to classify it to a sub-class type

The root and the sibling classifiers are configured depending on the input size and the number of classes- to be discriminated at each level This network as a whole is a supervised network which means the network is trained according to the desired response of the researcher

In this paper we have investigated these two methods of ANN for the classification of ruE stellar spectra The first method involves a single IvIBPN classifier to classify the test spectra into 75 spectro-luminosity classes The second method which in principle incorporates a divide-and-conquer technique is devised as a tree network The root node distinguishes the database into four main spectral types and then its children nodes further classified it into a total of 75 spectro-luminosity classes

In the first case the whole training set was presented to the network several times dtUing training until the network was able to discriminate all 75 classes In the case of the tree network the whole training set was presented to the root node to classify only four main spectral classes and then the subset of training set was presented to each sibling network to further classify it into sub-classes This tree network can be extended further to find many sub-class types if the database of any application provides the p~tterns upto those many sub-class types One advantage of IvITN over ANN is that it requires lesser time than ANN since after the initial root node classification it has to only classify the sibling nodes

4 Results and Discussion

Ve applied ANN comprising the 35 input nodes (n=35 monitoring frequency parameters) one hidden layer of (2n+l) nodes and outputs of 75 nodes representing the 75

spectro-luminosity classes to train the network The (2n+l) criterion is dictated by certain empirical facts and theoretical considerations which render an optimization on accuracy

- 11 shy

human ePerts

5 Conclusion

Ve have demonstrated that Neural Networks schemes based on multi layer back propagation method using single and multi-level tree configllrationsare able to classify 94 of the test sample of lTV spectra to one-sub class accuracy_ Vith these schemes 72 of the spectra were classified correctly in terms of luminosity which is otherwise a sore point of automated schemes Further improvement is required in the training part of the ANNs which should ultimately lead to greater classification accuracies ANNs will beconle

extremely handy for large database classifications which are otherwise outside the scope of human classification

Ve thank the ruCAA Astronomical Data Center for providing the spectral catalogs used in the current work Thanks are also due to Profs C Jaschek and lV1 Jaschek for their useful comments Ve are grateful to Prof K D Abhyankar for critically going through the manuscript This research has made use of the SIlVIBAD database operated at CDS Strasbourg France

- 12shy

Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

5000

4000

3000 zz lt

2000

1000

0 a 1000 2000 3000

Catalog 4000 5000

5000

4000

3000 z ~

2000

1000

a ~--~~~~~--~--~--~--~--~ a 1000 2000 3000 4000 5000

Catalog

50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

4000 40

rIJ

laquoS 3000 j 30

~ 0

2000 eQJ

20 = z

1000

1000 2000 3000 4000 5000

10

a

f

Catalog

5000

4000

3000

~

2000

1000

0 B A F a

-1000 -500 a 500 1000 Deviation (r)

50

40

f laquoS j 30 0 eQJ

20 s z

10

a

h

a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

60 60

In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

-5shy

to as x2-minimization scheme) on the IUE data only for comparing the performance of the ANN techniques This technique is based on the assumption that the spectrum consists of points in an n-dimensional vector space (where n is approximately the number of resolution elements in the spectrum) and the classification is based on finding the shortest distance from the unknown stars spectrum to a set of spectra of the standard stars The view of the observation space as a vector space lies at the heart of the various parametric methods of statistical comparison such as techniques based on reduced X2 which is defined as (for no statistical weighting Bevington (1969))

x2= Ef=l(S - Tt)2 (2)P

where p is equal to the degrees of freedom SiCA) is the spectrum for one of the set of standard star spectra and Ti(Ai) for the unknown stars spectrum Ai are the wavelengths with i = 1 n for n wavelength monitoring points as is described later in the paper The unknown stars spectrum (test spectrum) is compared with the set of reference spectra to compute a set of X2 values The spectral type of the reference spectrum corresponding to the minirrium X2 is assigned to the test spectrum This procedure is then repeated for the remaining set of the test spectra

32 Artificial Neural Networks Scheme

Artificial neural networks (hereafter ANNs) are computational models derived from the simulation of the human brain (IvlcCulloch and Pitts (1943) and Hopfield and Tank (1986)) These netrorks consist of a series of processing elements known as neurons or nodes arranged in layers These nodes are analogous to biological neurons with inputs (dendrites) summing nodes (soma or cell bodies) outputs (axons) and weighted connections between layers (synapses)

These networks have ability to learn from examples and store the information in weights in a generalized form This facilitates the appropriate classification ~f the input patterns which are not included in the training set provided the training set covered the representative patterns for all the claSses The features of ANN learning and generalization thus enable these networks for solving imaging and signal processing tasks which cannot be readily attacked using rule-based or other conventional techniques

Various ANN architectures and learning algorithms have been developed and are being used in academic research as well as in industrial applications A plenty of books and research papers onthis topic are available A few network architectures and learning rules have been reviewed by (Adorf (1989) Vidrow and Lehr (1990) and Clark (1991))

5

-6shy

Recently ANN algorithms are being used for arious astronomy applications including the classification of objects in the mAS Point Source Catalogue (Adorf and IYleurs (1988)) adaptive optics (Angel et al (1990)) star-galaxy separation (Odewahn et al (1992)) stellar spectral classification (von Hippel et al (1994) Gulati et al (1994)) morphological classification of galaxies (Storrie-Lombardi et al (1992)) and classification of interplanetary spectra (Gothoskar and Khobragade (1993)) IYlost of these astronomy applications using ANNs have been reviewed by (lfi11er (1993))

In astronomy applications so far researchers have used mainly two types of learning algorithms - a supervised backpropagation network (Rumelhart et al (1986)) and an unsupervised self-organizing map (Kohonen (1990)) Hybrid models using both strategies with and without supervision have also been developed such as the counter-propagation network (Hecht-Nielson (1987)) which are not yet employed in astronomy There are other models like hierarchical networks and tree networks (Sankar and IYlammone (1991)) 1

which are still away from the astronomy field Supervised learning requires researchers desired response during training which means these networks learn in supervision of the researcher Unsupervised learning requires no exemplar output or supervision

For this application we have investigated a conventional backpropagation network (hereafter IYIBPN) as a pattern classifier to discriminate the IDE stellar spectra into arious classes Ve have also attempted a tree-like network we call it as a multilevel tree network (hereafter IYITN) which employs the IYffiPN at the root and each non-terminal nodes of the tree

3 Bl The multilayer bac1cpropagation clGSsifier

The multilayer backpropagation network (Rumelhart et al (1986)) has several nodes arranged in a series of layers - an input layer one or more hidden layers and an output layer Input layer equals the size of the input pattern and the size of output layer is equal to the number of classes to be distinguished The size of the intermediate layers depends on the complexity of the problem to be solved The intermediate layers are also known as hidden lay~rs The network complexity is a function of the number of inputs hidden nodes layers outputs and connections (see Figure 2) It should be noted that the input layer is transparent in the sense that it receives the input pattern and distributes it to the next layer as it is without doing any computations The weighted connections between the layers are unidirectional and the information flows from the input layer through the output layer Hence it is also called a feedforward network A layer is fully connected if each node in the layer is connected to all the nodes in an adjacent layer However the complexity of

the netYork can be reduced by using partially connected layers

Learning the network means to find a set of weights which eventually store the learned patterns During learning the weights are first initialized to small random values The input pattern from the training set is then presented to the network The weighted input is summed over linearly at each node of the hidden layer and is passed through a non-linear sigmoid transfer function to get an actual output at each node using the existing set of weights The procedure is repeated for all the nodes in the hidden and output layers The resultant computed output is then compared with the desired output to get an error term which is propagated backward through the network to compute the changes of the interconnection Yeights between each pair of layers The weights are updated in such a way as to mjnimize the output error during the next time-step of the learning process The procedure is repeated for all the patterns in the training set and the weights are updated until the network output error mjnimizes to the specified threshold value The rate of updating of weights is controlled by a learning coefficient (gain factor) and a momentum factor a which damps the oscillations in the error minjmization process and furthermore both these parameters are dependent on the input patterns Veights can be updated after presenting each input pattern or after each presentation of the complete training set A plot of the error term against the number of presentations gives a learning curve~ which ideally converges to zerO as the number of presentations increases A training set consists of a variety of examples from each class to generalize the class information which is eventually stored in the weights The final set of weights are used to classify a large database which was not used during training

922 The multilevel tree network

Ve have attempted a new technique resembling a tree structure A three-level tree network is shown in Figure 3 This network terminology is analogous to that ofmiddota tree The very first node is called a root node which is at level one Nodes at level two which are children of root node again form subtrees Terminal nodes which are at last level are also called leaf nodes Children of the same parent node are known as siblings

The 1ITN uses the same 1ffiPN (described above) at root and non-terminal nodes Terminal nodes just label the final output class they do not employ the 1IBPN classifier

The learning algorithm for this network is derived as follows A complete training set is presented to the root node The classifier at the root node discrinlinates the whole training set into the main classes of different spectral types The outputs of the root node

7

-8shy

classifier represented as non-terminal nodes (see Figure 3) further use the lVIBPN over the reduced training set containing only the respective main-class spectra The siblings at level two can be computed conctUrently on different machines (if one has access to a netYork of work stations) The output of each individual sibling classifier which are represented by leaf nodes are used to label the class of the input pattern The yeights of root and siblings classifiers can be stored in separate files to use them for the application to unseen database

DtUing the application of this network the test pattern is first presented to the root node classifier which classifies it as one of the main classes Then the same pattern is applied to the respective class-sibling classifier to classify it to a sub-class type

The root and the sibling classifiers are configured depending on the input size and the number of classes- to be discriminated at each level This network as a whole is a supervised network which means the network is trained according to the desired response of the researcher

In this paper we have investigated these two methods of ANN for the classification of ruE stellar spectra The first method involves a single IvIBPN classifier to classify the test spectra into 75 spectro-luminosity classes The second method which in principle incorporates a divide-and-conquer technique is devised as a tree network The root node distinguishes the database into four main spectral types and then its children nodes further classified it into a total of 75 spectro-luminosity classes

In the first case the whole training set was presented to the network several times dtUing training until the network was able to discriminate all 75 classes In the case of the tree network the whole training set was presented to the root node to classify only four main spectral classes and then the subset of training set was presented to each sibling network to further classify it into sub-classes This tree network can be extended further to find many sub-class types if the database of any application provides the p~tterns upto those many sub-class types One advantage of IvITN over ANN is that it requires lesser time than ANN since after the initial root node classification it has to only classify the sibling nodes

4 Results and Discussion

Ve applied ANN comprising the 35 input nodes (n=35 monitoring frequency parameters) one hidden layer of (2n+l) nodes and outputs of 75 nodes representing the 75

spectro-luminosity classes to train the network The (2n+l) criterion is dictated by certain empirical facts and theoretical considerations which render an optimization on accuracy

- 11 shy

human ePerts

5 Conclusion

Ve have demonstrated that Neural Networks schemes based on multi layer back propagation method using single and multi-level tree configllrationsare able to classify 94 of the test sample of lTV spectra to one-sub class accuracy_ Vith these schemes 72 of the spectra were classified correctly in terms of luminosity which is otherwise a sore point of automated schemes Further improvement is required in the training part of the ANNs which should ultimately lead to greater classification accuracies ANNs will beconle

extremely handy for large database classifications which are otherwise outside the scope of human classification

Ve thank the ruCAA Astronomical Data Center for providing the spectral catalogs used in the current work Thanks are also due to Profs C Jaschek and lV1 Jaschek for their useful comments Ve are grateful to Prof K D Abhyankar for critically going through the manuscript This research has made use of the SIlVIBAD database operated at CDS Strasbourg France

- 12shy

Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

5000

4000

3000 zz lt

2000

1000

0 a 1000 2000 3000

Catalog 4000 5000

5000

4000

3000 z ~

2000

1000

a ~--~~~~~--~--~--~--~--~ a 1000 2000 3000 4000 5000

Catalog

50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

4000 40

rIJ

laquoS 3000 j 30

~ 0

2000 eQJ

20 = z

1000

1000 2000 3000 4000 5000

10

a

f

Catalog

5000

4000

3000

~

2000

1000

0 B A F a

-1000 -500 a 500 1000 Deviation (r)

50

40

f laquoS j 30 0 eQJ

20 s z

10

a

h

a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

60 60

In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

-6shy

Recently ANN algorithms are being used for arious astronomy applications including the classification of objects in the mAS Point Source Catalogue (Adorf and IYleurs (1988)) adaptive optics (Angel et al (1990)) star-galaxy separation (Odewahn et al (1992)) stellar spectral classification (von Hippel et al (1994) Gulati et al (1994)) morphological classification of galaxies (Storrie-Lombardi et al (1992)) and classification of interplanetary spectra (Gothoskar and Khobragade (1993)) IYlost of these astronomy applications using ANNs have been reviewed by (lfi11er (1993))

In astronomy applications so far researchers have used mainly two types of learning algorithms - a supervised backpropagation network (Rumelhart et al (1986)) and an unsupervised self-organizing map (Kohonen (1990)) Hybrid models using both strategies with and without supervision have also been developed such as the counter-propagation network (Hecht-Nielson (1987)) which are not yet employed in astronomy There are other models like hierarchical networks and tree networks (Sankar and IYlammone (1991)) 1

which are still away from the astronomy field Supervised learning requires researchers desired response during training which means these networks learn in supervision of the researcher Unsupervised learning requires no exemplar output or supervision

For this application we have investigated a conventional backpropagation network (hereafter IYIBPN) as a pattern classifier to discriminate the IDE stellar spectra into arious classes Ve have also attempted a tree-like network we call it as a multilevel tree network (hereafter IYITN) which employs the IYffiPN at the root and each non-terminal nodes of the tree

3 Bl The multilayer bac1cpropagation clGSsifier

The multilayer backpropagation network (Rumelhart et al (1986)) has several nodes arranged in a series of layers - an input layer one or more hidden layers and an output layer Input layer equals the size of the input pattern and the size of output layer is equal to the number of classes to be distinguished The size of the intermediate layers depends on the complexity of the problem to be solved The intermediate layers are also known as hidden lay~rs The network complexity is a function of the number of inputs hidden nodes layers outputs and connections (see Figure 2) It should be noted that the input layer is transparent in the sense that it receives the input pattern and distributes it to the next layer as it is without doing any computations The weighted connections between the layers are unidirectional and the information flows from the input layer through the output layer Hence it is also called a feedforward network A layer is fully connected if each node in the layer is connected to all the nodes in an adjacent layer However the complexity of

the netYork can be reduced by using partially connected layers

Learning the network means to find a set of weights which eventually store the learned patterns During learning the weights are first initialized to small random values The input pattern from the training set is then presented to the network The weighted input is summed over linearly at each node of the hidden layer and is passed through a non-linear sigmoid transfer function to get an actual output at each node using the existing set of weights The procedure is repeated for all the nodes in the hidden and output layers The resultant computed output is then compared with the desired output to get an error term which is propagated backward through the network to compute the changes of the interconnection Yeights between each pair of layers The weights are updated in such a way as to mjnimize the output error during the next time-step of the learning process The procedure is repeated for all the patterns in the training set and the weights are updated until the network output error mjnimizes to the specified threshold value The rate of updating of weights is controlled by a learning coefficient (gain factor) and a momentum factor a which damps the oscillations in the error minjmization process and furthermore both these parameters are dependent on the input patterns Veights can be updated after presenting each input pattern or after each presentation of the complete training set A plot of the error term against the number of presentations gives a learning curve~ which ideally converges to zerO as the number of presentations increases A training set consists of a variety of examples from each class to generalize the class information which is eventually stored in the weights The final set of weights are used to classify a large database which was not used during training

922 The multilevel tree network

Ve have attempted a new technique resembling a tree structure A three-level tree network is shown in Figure 3 This network terminology is analogous to that ofmiddota tree The very first node is called a root node which is at level one Nodes at level two which are children of root node again form subtrees Terminal nodes which are at last level are also called leaf nodes Children of the same parent node are known as siblings

The 1ITN uses the same 1ffiPN (described above) at root and non-terminal nodes Terminal nodes just label the final output class they do not employ the 1IBPN classifier

The learning algorithm for this network is derived as follows A complete training set is presented to the root node The classifier at the root node discrinlinates the whole training set into the main classes of different spectral types The outputs of the root node

7

-8shy

classifier represented as non-terminal nodes (see Figure 3) further use the lVIBPN over the reduced training set containing only the respective main-class spectra The siblings at level two can be computed conctUrently on different machines (if one has access to a netYork of work stations) The output of each individual sibling classifier which are represented by leaf nodes are used to label the class of the input pattern The yeights of root and siblings classifiers can be stored in separate files to use them for the application to unseen database

DtUing the application of this network the test pattern is first presented to the root node classifier which classifies it as one of the main classes Then the same pattern is applied to the respective class-sibling classifier to classify it to a sub-class type

The root and the sibling classifiers are configured depending on the input size and the number of classes- to be discriminated at each level This network as a whole is a supervised network which means the network is trained according to the desired response of the researcher

In this paper we have investigated these two methods of ANN for the classification of ruE stellar spectra The first method involves a single IvIBPN classifier to classify the test spectra into 75 spectro-luminosity classes The second method which in principle incorporates a divide-and-conquer technique is devised as a tree network The root node distinguishes the database into four main spectral types and then its children nodes further classified it into a total of 75 spectro-luminosity classes

In the first case the whole training set was presented to the network several times dtUing training until the network was able to discriminate all 75 classes In the case of the tree network the whole training set was presented to the root node to classify only four main spectral classes and then the subset of training set was presented to each sibling network to further classify it into sub-classes This tree network can be extended further to find many sub-class types if the database of any application provides the p~tterns upto those many sub-class types One advantage of IvITN over ANN is that it requires lesser time than ANN since after the initial root node classification it has to only classify the sibling nodes

4 Results and Discussion

Ve applied ANN comprising the 35 input nodes (n=35 monitoring frequency parameters) one hidden layer of (2n+l) nodes and outputs of 75 nodes representing the 75

spectro-luminosity classes to train the network The (2n+l) criterion is dictated by certain empirical facts and theoretical considerations which render an optimization on accuracy

- 11 shy

human ePerts

5 Conclusion

Ve have demonstrated that Neural Networks schemes based on multi layer back propagation method using single and multi-level tree configllrationsare able to classify 94 of the test sample of lTV spectra to one-sub class accuracy_ Vith these schemes 72 of the spectra were classified correctly in terms of luminosity which is otherwise a sore point of automated schemes Further improvement is required in the training part of the ANNs which should ultimately lead to greater classification accuracies ANNs will beconle

extremely handy for large database classifications which are otherwise outside the scope of human classification

Ve thank the ruCAA Astronomical Data Center for providing the spectral catalogs used in the current work Thanks are also due to Profs C Jaschek and lV1 Jaschek for their useful comments Ve are grateful to Prof K D Abhyankar for critically going through the manuscript This research has made use of the SIlVIBAD database operated at CDS Strasbourg France

- 12shy

Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

5000

4000

3000 zz lt

2000

1000

0 a 1000 2000 3000

Catalog 4000 5000

5000

4000

3000 z ~

2000

1000

a ~--~~~~~--~--~--~--~--~ a 1000 2000 3000 4000 5000

Catalog

50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

4000 40

rIJ

laquoS 3000 j 30

~ 0

2000 eQJ

20 = z

1000

1000 2000 3000 4000 5000

10

a

f

Catalog

5000

4000

3000

~

2000

1000

0 B A F a

-1000 -500 a 500 1000 Deviation (r)

50

40

f laquoS j 30 0 eQJ

20 s z

10

a

h

a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

60 60

In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

the netYork can be reduced by using partially connected layers

Learning the network means to find a set of weights which eventually store the learned patterns During learning the weights are first initialized to small random values The input pattern from the training set is then presented to the network The weighted input is summed over linearly at each node of the hidden layer and is passed through a non-linear sigmoid transfer function to get an actual output at each node using the existing set of weights The procedure is repeated for all the nodes in the hidden and output layers The resultant computed output is then compared with the desired output to get an error term which is propagated backward through the network to compute the changes of the interconnection Yeights between each pair of layers The weights are updated in such a way as to mjnimize the output error during the next time-step of the learning process The procedure is repeated for all the patterns in the training set and the weights are updated until the network output error mjnimizes to the specified threshold value The rate of updating of weights is controlled by a learning coefficient (gain factor) and a momentum factor a which damps the oscillations in the error minjmization process and furthermore both these parameters are dependent on the input patterns Veights can be updated after presenting each input pattern or after each presentation of the complete training set A plot of the error term against the number of presentations gives a learning curve~ which ideally converges to zerO as the number of presentations increases A training set consists of a variety of examples from each class to generalize the class information which is eventually stored in the weights The final set of weights are used to classify a large database which was not used during training

922 The multilevel tree network

Ve have attempted a new technique resembling a tree structure A three-level tree network is shown in Figure 3 This network terminology is analogous to that ofmiddota tree The very first node is called a root node which is at level one Nodes at level two which are children of root node again form subtrees Terminal nodes which are at last level are also called leaf nodes Children of the same parent node are known as siblings

The 1ITN uses the same 1ffiPN (described above) at root and non-terminal nodes Terminal nodes just label the final output class they do not employ the 1IBPN classifier

The learning algorithm for this network is derived as follows A complete training set is presented to the root node The classifier at the root node discrinlinates the whole training set into the main classes of different spectral types The outputs of the root node

7

-8shy

classifier represented as non-terminal nodes (see Figure 3) further use the lVIBPN over the reduced training set containing only the respective main-class spectra The siblings at level two can be computed conctUrently on different machines (if one has access to a netYork of work stations) The output of each individual sibling classifier which are represented by leaf nodes are used to label the class of the input pattern The yeights of root and siblings classifiers can be stored in separate files to use them for the application to unseen database

DtUing the application of this network the test pattern is first presented to the root node classifier which classifies it as one of the main classes Then the same pattern is applied to the respective class-sibling classifier to classify it to a sub-class type

The root and the sibling classifiers are configured depending on the input size and the number of classes- to be discriminated at each level This network as a whole is a supervised network which means the network is trained according to the desired response of the researcher

In this paper we have investigated these two methods of ANN for the classification of ruE stellar spectra The first method involves a single IvIBPN classifier to classify the test spectra into 75 spectro-luminosity classes The second method which in principle incorporates a divide-and-conquer technique is devised as a tree network The root node distinguishes the database into four main spectral types and then its children nodes further classified it into a total of 75 spectro-luminosity classes

In the first case the whole training set was presented to the network several times dtUing training until the network was able to discriminate all 75 classes In the case of the tree network the whole training set was presented to the root node to classify only four main spectral classes and then the subset of training set was presented to each sibling network to further classify it into sub-classes This tree network can be extended further to find many sub-class types if the database of any application provides the p~tterns upto those many sub-class types One advantage of IvITN over ANN is that it requires lesser time than ANN since after the initial root node classification it has to only classify the sibling nodes

4 Results and Discussion

Ve applied ANN comprising the 35 input nodes (n=35 monitoring frequency parameters) one hidden layer of (2n+l) nodes and outputs of 75 nodes representing the 75

spectro-luminosity classes to train the network The (2n+l) criterion is dictated by certain empirical facts and theoretical considerations which render an optimization on accuracy

- 11 shy

human ePerts

5 Conclusion

Ve have demonstrated that Neural Networks schemes based on multi layer back propagation method using single and multi-level tree configllrationsare able to classify 94 of the test sample of lTV spectra to one-sub class accuracy_ Vith these schemes 72 of the spectra were classified correctly in terms of luminosity which is otherwise a sore point of automated schemes Further improvement is required in the training part of the ANNs which should ultimately lead to greater classification accuracies ANNs will beconle

extremely handy for large database classifications which are otherwise outside the scope of human classification

Ve thank the ruCAA Astronomical Data Center for providing the spectral catalogs used in the current work Thanks are also due to Profs C Jaschek and lV1 Jaschek for their useful comments Ve are grateful to Prof K D Abhyankar for critically going through the manuscript This research has made use of the SIlVIBAD database operated at CDS Strasbourg France

- 12shy

Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

5000

4000

3000 zz lt

2000

1000

0 a 1000 2000 3000

Catalog 4000 5000

5000

4000

3000 z ~

2000

1000

a ~--~~~~~--~--~--~--~--~ a 1000 2000 3000 4000 5000

Catalog

50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

4000 40

rIJ

laquoS 3000 j 30

~ 0

2000 eQJ

20 = z

1000

1000 2000 3000 4000 5000

10

a

f

Catalog

5000

4000

3000

~

2000

1000

0 B A F a

-1000 -500 a 500 1000 Deviation (r)

50

40

f laquoS j 30 0 eQJ

20 s z

10

a

h

a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

60 60

In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

-8shy

classifier represented as non-terminal nodes (see Figure 3) further use the lVIBPN over the reduced training set containing only the respective main-class spectra The siblings at level two can be computed conctUrently on different machines (if one has access to a netYork of work stations) The output of each individual sibling classifier which are represented by leaf nodes are used to label the class of the input pattern The yeights of root and siblings classifiers can be stored in separate files to use them for the application to unseen database

DtUing the application of this network the test pattern is first presented to the root node classifier which classifies it as one of the main classes Then the same pattern is applied to the respective class-sibling classifier to classify it to a sub-class type

The root and the sibling classifiers are configured depending on the input size and the number of classes- to be discriminated at each level This network as a whole is a supervised network which means the network is trained according to the desired response of the researcher

In this paper we have investigated these two methods of ANN for the classification of ruE stellar spectra The first method involves a single IvIBPN classifier to classify the test spectra into 75 spectro-luminosity classes The second method which in principle incorporates a divide-and-conquer technique is devised as a tree network The root node distinguishes the database into four main spectral types and then its children nodes further classified it into a total of 75 spectro-luminosity classes

In the first case the whole training set was presented to the network several times dtUing training until the network was able to discriminate all 75 classes In the case of the tree network the whole training set was presented to the root node to classify only four main spectral classes and then the subset of training set was presented to each sibling network to further classify it into sub-classes This tree network can be extended further to find many sub-class types if the database of any application provides the p~tterns upto those many sub-class types One advantage of IvITN over ANN is that it requires lesser time than ANN since after the initial root node classification it has to only classify the sibling nodes

4 Results and Discussion

Ve applied ANN comprising the 35 input nodes (n=35 monitoring frequency parameters) one hidden layer of (2n+l) nodes and outputs of 75 nodes representing the 75

spectro-luminosity classes to train the network The (2n+l) criterion is dictated by certain empirical facts and theoretical considerations which render an optimization on accuracy

- 11 shy

human ePerts

5 Conclusion

Ve have demonstrated that Neural Networks schemes based on multi layer back propagation method using single and multi-level tree configllrationsare able to classify 94 of the test sample of lTV spectra to one-sub class accuracy_ Vith these schemes 72 of the spectra were classified correctly in terms of luminosity which is otherwise a sore point of automated schemes Further improvement is required in the training part of the ANNs which should ultimately lead to greater classification accuracies ANNs will beconle

extremely handy for large database classifications which are otherwise outside the scope of human classification

Ve thank the ruCAA Astronomical Data Center for providing the spectral catalogs used in the current work Thanks are also due to Profs C Jaschek and lV1 Jaschek for their useful comments Ve are grateful to Prof K D Abhyankar for critically going through the manuscript This research has made use of the SIlVIBAD database operated at CDS Strasbourg France

- 12shy

Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

5000

4000

3000 zz lt

2000

1000

0 a 1000 2000 3000

Catalog 4000 5000

5000

4000

3000 z ~

2000

1000

a ~--~~~~~--~--~--~--~--~ a 1000 2000 3000 4000 5000

Catalog

50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

4000 40

rIJ

laquoS 3000 j 30

~ 0

2000 eQJ

20 = z

1000

1000 2000 3000 4000 5000

10

a

f

Catalog

5000

4000

3000

~

2000

1000

0 B A F a

-1000 -500 a 500 1000 Deviation (r)

50

40

f laquoS j 30 0 eQJ

20 s z

10

a

h

a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

60 60

In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

- 11 shy

human ePerts

5 Conclusion

Ve have demonstrated that Neural Networks schemes based on multi layer back propagation method using single and multi-level tree configllrationsare able to classify 94 of the test sample of lTV spectra to one-sub class accuracy_ Vith these schemes 72 of the spectra were classified correctly in terms of luminosity which is otherwise a sore point of automated schemes Further improvement is required in the training part of the ANNs which should ultimately lead to greater classification accuracies ANNs will beconle

extremely handy for large database classifications which are otherwise outside the scope of human classification

Ve thank the ruCAA Astronomical Data Center for providing the spectral catalogs used in the current work Thanks are also due to Profs C Jaschek and lV1 Jaschek for their useful comments Ve are grateful to Prof K D Abhyankar for critically going through the manuscript This research has made use of the SIlVIBAD database operated at CDS Strasbourg France

- 12shy

Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

5000

4000

3000 zz lt

2000

1000

0 a 1000 2000 3000

Catalog 4000 5000

5000

4000

3000 z ~

2000

1000

a ~--~~~~~--~--~--~--~--~ a 1000 2000 3000 4000 5000

Catalog

50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

4000 40

rIJ

laquoS 3000 j 30

~ 0

2000 eQJ

20 = z

1000

1000 2000 3000 4000 5000

10

a

f

Catalog

5000

4000

3000

~

2000

1000

0 B A F a

-1000 -500 a 500 1000 Deviation (r)

50

40

f laquoS j 30 0 eQJ

20 s z

10

a

h

a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

60 60

In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

- 12shy

Parameters Catalog vs X2 Catalog vs ANN Catalog vs ~ITN ANN vs X2

a 1288 1060 1162 8385 mplusmn Qm 1037 plusmn 0025 1018 plusmn 0021 1022 plusmn 0023 0998 plusmn0017 c plusmn Qc -9999 plusmn 6507 -5872 plusmn 5395 -5860 plusmn 5952 511 plusmn 4263 r 09776 09839 09810 09901

Table 1 Comparative Performance of Classification Schemes (after 3-0 rejection)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

5000

4000

3000 zz lt

2000

1000

0 a 1000 2000 3000

Catalog 4000 5000

5000

4000

3000 z ~

2000

1000

a ~--~~~~~--~--~--~--~--~ a 1000 2000 3000 4000 5000

Catalog

50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

4000 40

rIJ

laquoS 3000 j 30

~ 0

2000 eQJ

20 = z

1000

1000 2000 3000 4000 5000

10

a

f

Catalog

5000

4000

3000

~

2000

1000

0 B A F a

-1000 -500 a 500 1000 Deviation (r)

50

40

f laquoS j 30 0 eQJ

20 s z

10

a

h

a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

60 60

In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

- 13 ~

REFERENCES

Adorf H NL (1986) Classification of Lor-resolution stellar spectra via template matchingshya simulation study In Data Analysis in Astronomy II V Eds Di Gesu V Scarsi L Crane P Friedman J H Levialdi S pp 61-69 Plenum Press NY lTSA

Adorf H NI (1989) Connectionism and Neural Networks In Knowledge-based systems in Astronomy Eds Heck A NIurtagh F pp 215-245 Springer-Terlag Heidelberg Germany

Adorf HNL Johnston NLD (1988) Artificial Neural Nets in Astronomy In Proc Workshop Konnelctionismus Eds Lischka C 329 pp 3-5 Kindermann J Arbeitspariere der GNID Bonn Germany

Adorf H1L IvIeurs EJA (1988) Supervised and Unsupervised Classification - The Case of RAS Point Sources In Large Scale Structures in the Universe Observational and Analytical Methods Eds Seither VC Duerbeck HIvL Tacke ~L pp 315-322 Springer-Verlag Heidelberg Germany

Angel JRP Vizinowich P Lloyd-Hart NL Sander D (1990) Adaptive Optics for Array Telescopes using Neural Network Techniques Nature 348 11-214

Bevington P R (1969) In Data Reduction and Error Analysis for the Physical Sciences Chapter 1-5 pp 1-91 IvlcGraw-Hill NY USA

Boggess A et ale (1978a) The ruE spacecraft and instrumentation Nature 275 372-377

Boggess A et ale (1978b) In-flight performance of the ruE Nature 275 377-385

Clark JV (1991) Neural Network NIodelling Phys Med BioI 36(1)1259-1317

Geva S Sitte J (1992) IEEE Transactions on Neural Networks 3621

Gothoskar P Khobragade S (1993) Classification of Interplanetary Stellar Spectra using Artificial Neural Network In Proc of the Int Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics Eds Joselyn J Lundstedt H Trolinger J pp 109-114

Gulati RK IvIalagnini NLL NIorossi C (1987) E(B-V) determination from an UV-visual two color diagram 0 and B stars in the Catalogue of Stellar Ultraviolet FhLes J Astroph Astron 8 315-329

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

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Levell

Sibling

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01 30 0 eQ)

20 = z

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a

b

50

d

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02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

505000

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laquoS 3000 j 30

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Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

- 14shy

Gulati RI( Gupta R Gothoskar P I(hobragade S (1994) Stellar spectral classification using automated schemes Astrophys J 426(1)340-344

Hecht-Nielsen (1987) Counter-Propagation Netrorks In Proc First Int Conf on Neural Networks 2pp 19-32 IEEE 87TH0191-7JuneSan Diego CA USA

Heck A Egret D Jaschek NI Jaschek C (1984) IUE Lor-Resolution Spectra a Reference Atlas-Part I Normal Stars ESA SP-l05

Heck A Egret D Nobelis PH Turlot J C (1986) Statistical confirmation of the UV Spectral classification system based on IUE low-dispersion stellar spectra Astrophys Space Sci 129 223-237

von Hippel T Storrie-Lombardi L J Storrie~Lombardi NI C (1994) Automated classification of stellar spectra where are we nor In The MK Process at 50 years A powerful tool for astrophysical insight Sept0-24 1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 289 San Francisco California USA

Hopfield JJ Tank DV (1986) Computing vith Neural Circuits A model Science 223 625-633

Jaschek 11 Jaschek C (1984) Classification of Ultraviolet Spectra in The MK Process and

Stellar Classification Ed Garrison R F pp 290-304 David Dunlap Observatory Toronto Canada

Jaschek C Jaschek NI (1990) In The Classification of Stars Cambridge University Press Cambridge UK

Kohonen T (1990) The Self-organizing NIap IEEE Proc 78(9) 1464-1480

Kurtz NI J (1984) Progress in automation techniques for 1IK classification In The iVfI( Process and Stellar Classification Ed Garrison R F pp 136-152 David Dunlap Observatory Toronto Canada

NIcCulloch VS Pitts V (1943) A logical calculus of the ideas immanent in nervous activity Bull Math Biophys 5 115-133

1Iiller AS (1993) A Review of Neural Network Applications in Astronomy Vistas in Astronomy 36 141-161

~Iurtagh F (1991) NeuTOcomputing 2183

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

NonTerminal

Nodes I I I I I I

______________________________________________________ -------______ 1I

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50

40

02 laquoS

01 30 0 eQ)

20 = z

10

a

b

50

d

40

02 laquoS

01 30 0 Q)

~ 20 = z

10

o ~~~----~--~~~--~~--~~~ -1000 -500 0 500 1000

-1000 -500 0 500 1000 Deviation (ANN)

Deviation (MTN)

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laquoS 3000 j 30

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a 1000 2000 3000 4000 5000 -1000 -500 a 500 1000 ANN Deviation

0

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In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

- 13shy

Odeyahn SC Stockvell EB~ Pennington RL Humphreys R~I Zumach VA (1992) Automated StarGalaAJ T Discrimination vith Neural Networks Astron J 103(1) 318-331

Rountree J Sonneborn G (1991) Criteria for the spectral classification in the ultraviolet Astrphys J 369 515-328

Rumelhart DE Hinton GE Villiams RJ (1986) Learning Representations by Back-Propagation Errors Nature 323 533-536

Sankar A 11ammone RJ (1991) In Neural Tree Networks Eds ~1ammone RJ Zeevi Y pp 281-302 Academic Press NY USA

Storrie-Lombardi wLC Lahav 0 Sodre Jr L Storrie-Lombardi LJ (1992) wIorphological classification of galaCies by Artificial Neural Networks Mon Not R Astron Soc

2598-12

Veaver Vm B (1994) Neural network classification of normal VN and A-type stars In The MK Process at 50 years A powerful tool for astrophysical nsight Sept 20-24

1999 Tucson Arizona Eds Corbally C J et al ASP Conf Series 60 pp 303 San Francisco California USA

Vidrow B Lehr rd A (1990) 30 Years of Adaptive Neural Networks Perception wladHne and Back-propagation Proc IEEE 18(9) 1415-1441

Figure Captions

Figure 1 Four examples of the template ultraviolet spectra used to train the network Vertical lines indicate the 35 monitoring wavelengths which vere used to derive the 35 filL(es as input to the network

Figure 2 A fully connected backpropagation network vith one hidden layer Nodes applying activation functions are shorn as circles Non-contributing nodes are shown as squares

Figure 3 A three-level tree netyork A circle represents a node employing 1IBPN A

square represents a node just for labeling the output class

Figure 4 Scatter plots and corresponding histograms of deviations for ANN vs catalog in (a) and (b) NITN vs catalog in (c) and (d) X2 VS catalog in (e) and (f) X2 vs ANN in (g) and (h) ( See text for details)

This preprint W(l5 prepared with the AAS 1-TEX macros v30

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

Sibling

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Nodes I I I I I I

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20 = z

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02 laquoS

01 30 0 Q)

~ 20 = z

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Deviation (MTN)

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In In GS GS rn 40 fshy rn 40Il104

Il104 0 QJ QJtJ e tJ

2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

80 c

rn 40 Il104 o

O~~~~~~~~~~~~ -5 0 5

Deviation in Luminosity (MTN)

- 16shy

Figure 5 Histograms for luminosity classification in terms of deviations from the catalog luminosity for X2 in (a) ANN in (b) and JITN in (c) Each bin corresponds to 3 luminosity units

3

Fluxes (Arbitrary Units)

o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

Levell

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In In GS GS rn 40 fshy rn 40Il104

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2 e 2 z 20 Z 20

o~~~~~~~~~~ -5 0 5 Deviation in Luminosity (XZ)

Deviation in Luminosity (ANN)

b

0~~_5~~ZQ~aO~~~~~5~~~

t GS

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rn 40 Il104 o

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3

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o 1 2

o I ~ 0

CD

=E C ltCD CD l C t+shyr ~

~ -

(Jl o o

fJ 0 0 0

- (Jl 0 0

tN o o o

3 0 l- r+ 0 J to

E c ltCD CD J to r+ T en

---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

_________________________________________________________ I

1r~2

-------------------------------------------------~------------------

Level 3 Terminal Nodes

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In In GS GS rn 40 fshy rn 40Il104

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b

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---------------------------------------------------------

middot

75 Outputs

Output Layer

Hidden Layer I I

(71 Nodes) I )

I

Weighted Connection I I I 1

3S-feature Input 1

t I

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1r~2

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